1001
1 INTRODUCTION
Inland navigation, due to its nature, has a number of
navigational limitations, including shallow water,
limited width of the waterway and bridge clearance.
The Classification of European Inland Waterways,
applied to large European rivers that are part of the
Trans-European Inland Waterway network, created by
the European Conference of Ministers of Transport
(ECMT) in 1992, refer to the main dimensions of
maximum vessel that is able to use the waterway. The
minimum air draft of bridges on the waterway,
dimensions of infrastructure crossing the waterway
like pipelines and locks, relate directly to the size of
vessels [15]. The shallowing of inland and port waters
caused by climate changes deepens the problem of
operational constraints when navigating in confined
waters, which in turn has a major impact on port
design [7]. The power-propulsion characteristics of
inland vessels should be sufficient to overcome the
river current. Very good manoeuvrability is required
to effectively counteract the danger of collisions with
hydrotechnical structures, sandbanks or shallows, and
floating objects. Due to the shallow draft and large
length to breadth ratio river vessels have poor course
keeping ability under lateral wind and poor turning
characteristics respectively. The usual solution to this
problem is a passive bow rudder or bow thruster - built
into the hull or attached to the first barge in the convoy
in independent floating bow. However, both solutions
have their limitations.
The paper focuses on the ability of an inland unit to
maintain the course, in unfavourable conditions, by
drift angle control, using an active auxiliary bow
steering device - the bow rotor rudder, adapted to
shallow water conditions. The presented research is a
continuation of the earlier numerical and experimental
studies on push convoy bow steering system [1, 3].
The proposed bow rotor rudder, presented in the
paper, which does not protrude beyond the ship's
bottom, differs from the existing solution of “Rotor
Manoeuvring System” (RMS), increasing the required
under-keel clearance at the bow by 1.2 m in the
operating position. Increasing course stability, RMS
helps to overcome lateral wind and can partly replace
Reduction of a Push Convoy Manoeuvring Space
in Inland Navigation by Drift Angle Control Using
the Bow Active Rudder
T. Abramowicz-Gerigk, Z. Burciu & A. Hejmlich
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: The inland vessels, barges and especially convoys are facing problems related to their
manoeuvrability in restricted waters. The paper presents an auxiliary steering device significantly improving
manoeuvrability and reducing the required manoeuvring space of a shallow draft inland vessels. The principle
of operation of the proposed active bow rudder is based on Magnus effect - the Magnus force generated on the
rotating cylinder (rotor). The presented research, based on physical model tests, confirmed the applicability of
the proposed solution. The results indicate a significant improvement in the manoeuvrability of vessels and
pushed convoys due to the reduction of manoeuvring space by drift angle control.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 3
September 2025
DOI: 10.12716/1001.19.03.35
1002
steering with a conventional rudder at speeds above 6
km/h, which results in lower ship resistance and lower
fuel consumption. Originally developed in the 1980s by
Van der Velden and modernised by Damen [19, 21] is
now getting more popular in inland shipping on large
river vessels
The analysis based on the results of the model tests,
presented in the paper, have confirmed the bow rotor
rudder suitability to control the drift angle. The
steering force estimated from tests was lower than the
determined using empirical methods. The main
reasons of the loss of the lift force are flow disturbances
around the rotating cylinder and vibrations at higher
rotational speeds. The conclusions presented in the
paper are related to the change of pivot point position
during manoeuvres when using the bow rotor rudder.
There is a suggestion of further experimental research
in towing tank to measure the real values of forces
generated on the rotor placed close to the water
surface.
2 SAFE MANOEUVRING SPACE IN INLAND
NAVIGATION - WATERWAY WIDTH
Several empirical methods are available to determine
the safe width of inland fairways [8, 12, 13, 14]. They
are tailored to the environment conditions, possible
interaction effects. They are presented as a function of
ship's design breadth and correction factors e.g.
manoeuvring component needed to accommodate the
ship's drift angle, changes of position due to the ship
response to the rudder and engine settings, margins for
bank suction, squat and potential errors. Additional
width is required at bends related to the ship's turning
radius and drift angle during the turn.
2.1 Design width of the waterway
The examples of the empirical methods, used in
concept and preliminary design, for the determination
of waterway width d, necessary for safe maneuvering,
in function of the ship's breadth are the Panama Canal
method [18], PIANC method [10, 12], Canadian
method [6] and ASCE method [4].
Panama Canal Method [18] can be applied when
using accurate navigation systems, securing the
continuous positioning of the ship on the assumed
trajectory [13]. The waterway width in this method is
determined as follows (1):
2
r
d kB d=+
(1)
where:
d - waterway width [m],
k – coefficient determined experimentally,
B – ship design breadth [m],
dr – lane width reserve [m].
Using the PIANC method (2) [13] the waterway
width d can be calculated in dependence of the basic
lane width, additional lane width corrections and
reserves on the right and left sides of the waterway.
9
1
m i rz rc
i
d d d d d
=
= + + +
(2)
where:
dm – basic lane width [m],
di – additional lane width correction [m],
drz – right lane width reserve [m],
drc – left lane width reserve [m].
2.2 Widening of the waterway on the bend
The radius of curvature and width of the river bend
significantly impact safety of navigation and require
careful consideration when evaluating waterway
suitability. High navigation risks can be expected due
to increased flow-induced drift and vessel instability.
A wide river with large bend radius offer better
navigation conditions. Sharp bends, with R/B values
below 3, are considered to pose greater risks [14].
In the Canadian method [14] used for the
determination of the waterway width on a bend, the
manoeuvring component on the bend dmz (4) is
dependent on navigation parameters of the waterway:
the traffic lane width on its linear section dm and
widening of the lane on the bend Δd:
mz m
d d d= +
(4)
where:
dmz – maneuvering component of the width of the
waterway on the bend [m],
dm – maneuvering component of the waterway width
on the linear section [m],
d – widening of the waterway on the bend [m],
without taking into account hydrometeorological
conditions.
Widening of the waterway on the bend and
parameters used to determine the width of the safe
manoeuvring area on a bend are presented in Figure 1.
Figure 1. Determination of the width of the maneuvering
area on a waterway bend.
Developed on the basis of [13].
22
3. 4551
oz
v L F
d
R K s
=
(5)
where
∆ψ - turning angle on a bend [
o
],
v - ship speed [m/s],
L - ship length [m],
F - coefficient equal to 1 - for one-way traffic, 2 - for
two-way traffic,
Ro - average curvature radius on a bend [m],
Kz - ship's course keeping ability coefficient (1 - poor, 2
- good, 3 - very good),
s - minimum required visibility from the ship's bridge
[m], s≥ 2446 m.
1003
Extra width in bends, according to PIANC Report
WG 141 [13], assuming quasi steady motion, when the
vessel is turned by the drift angle against its course, is
predicted as follows (6):
2
/
c c o
b c L R L =
(6)
The parameter cc, equal to sinβ (6), where β is the
ship’s drift angle, is geometrically related to the
relative position of tactical turning point PP (pivot
point).
sin(β) = (cF-0.5)∙L (7)
where:
cF – distance between stern and PP, divided by the ship
length.
cc depends on ship draft to water depth ratio T/h,
ship breadth to length ratio B/L and ship movement
direction - upstream or downstream the river. It can be
assumed for the single way traffic equal to 0.25 for
loaded and 0.5 for empty vessels. However in practice
it can be bigger or smaller e.g. in case of the use of bow
thrusters [13].
For large drift angles when PP is located ahead of
the bow cF is greater than 1. The rounded values of cc
are equal to: cc=0.5 cF
2
for cF ≤1 and cc=-0.5 for cF>1.
cF may be reduced by about 0.1 - 0.2 in case the strong
bow thruster is used [13].
The design waterway width is related to the
navigation restrictions e.g. the ship’s speed, mainly
due to the wake wash. The propulsion-induced
impacts e.g. bottom erosion from propellers at low
speeds can be higher as the thrust streams are not
deflected by the ship induced flow. The proposed bow
rotor rudder can be used at higher speeds than bow
thrusters, generating a hydrodynamic force dependent
on the drift angle – with different components of drag
and lift. This is very important for maintaining course
and turning in the event of a strong crosswind.
2.3 Maneuvering space of a pushed convoy in inland
waterborne transport
The essence of a push or towed barge convoys is to
separate the engine room with the propulsion system
from the part intended for loading. In inland waterway
transport pushed convoys consisted of a pusher and a
pushed barge system are much more often used than
towed convoys. Compared to the towed convoy, the
pushed convoy has several advantages:
− reduced water resistance in relation to the
deadweight,
− fewer crew members,
− possibility of many configurations of pusher-barges
sets,
− reduced building costs,
− improved maneuverability,
− reduced turning area.
The disadvantages comparing to the pushed
convoy include the higher risk of collisions with
structures and floating objects, touching the river bed
or grounding.
Maneuvering on inland waterways can be
compared to maritime navigation in confined waters,
with low vessel proximity to shore or seabed. The
width of the waterway is determined by the breadth
and drift angle of the vessel navigating under the
strong lateral wind. The drift angle depends on the
following factors:
− radius of the bend,
− speed of the vessel,
− powering of the vessel, auxiliary steering devices
e.g. bow thruster, bow rudder
− loading condition of the vessel,
− hydrometeorological conditions: wind parameters,
water currents, turbulence, high/low water level,
− direction of the vessel movement - downstream or
upstream the river,
− training measures, piloting systems and decision
support systems.
The size and manoeuvring characteristics of the
push convoy are the most influencing factors in
determination of the required waterway with in the
river bend. The maneuvering space on a waterway
bend is also dependent on the method of connecting
barges into a push convoy [1]. Drift angle for push
convoys of different sizes being towed downstream in
a 3000-foot turn (914 m) was presented in [9] and [16]
(Figure 2).
Figure 2. Drift angle for convoys of different sizes sailing
downstream in a bend of 3000-foot radius R (914 m): αb - drift
angle, W - channel width dependent on the convoy
dimensions and drift angle. Developed based on [9]
originally presented by [16].
To navigate the bends the large drift angle created
by helmsman is necessary to generate the transverse
component of the hydrodynamic force and yawing
moment, therefore the upstream sailing convoys need
smaller waterway width due to the smaller speed over
ground and smaller sideways displacement, resulting
with the speed multiplied by the helmsman reaction
time to the drift angles.
The forces generated by a bow rudder or bow
thruster installed on the barge in front of the convoy
1004
can decrease the necessary drift angle and necessary
waterway width. However, these forces are much
smaller than the hydrodynamic force on the hull and
they can be insufficient to decrease the required drift
angle. In shallow water conditions hydrodynamic
forces and necessary drift angles are larger resulting in
further increase of the necessary waterway width [13].
The bow thruster force FBT in dependence of sip
velocity in shallow water FBT and canals FBTC (8) is
presented in Figure 3 [13].
0
0
1
BTC BT
C
v
FF
v
=−
(8)
Figure 3. Bow thruster force FBT in dependence of sip velocity:
FBT0 – bow thruster force for v=0, v0 – ship speed in shallow
water where FBT vanishes, v0C – reduced v0 in canals due to
the return current, Developed on the basis of [13].
Using the bow rotor rudder, generating the large
steering force at higher speeds, allows to decrease the
necessary drift angle and the required waterway
width.
3 USING THE MAGNUS EFFECT TO REDUCE THE
MANOEUVRING SPACE OF THE PUSHED
CONVOY
The Magnus effect is the phenomenon of generating lift
force on a rotating cylinder. The theoretical value of the
lift force calculated per cylinder length unit in
incompressible, steady inviscid flow can be
determined by Kutta-Joukowski law (9).
( )
x
L
Fv
=
(9)
where:
FL - lift force [N],
ρ - fluid density [kg/m
3
],
v - relative speed of fluid [m/s],
Γ - circulation around the cylinder [m
2
/s] (10):
2
2πar=
(10)
where:
a - rotor radius [m],
r - rotational speed of the cylinder [rad/s].
The lift force calculated using formula (9) is much
greater than the real rotor-generated force, which is
dependent on flow characteristics i.a. interaction
effects, free surface effect, flow separation and edge
losses.
In real conditions the lift force for the rotor fully
submerged can be calculated using formula (11) [12].
2
LL
F C v a
=
(11)
where:
CL(Re, α) - lift force coefficient (12) [11],
/ra v
=
(12)
If the rotor is installed in the bow part of the shallow
draft vessel, does not protrude beyond the bottom and
its upper edge is close to the free surface, the actual lift
force can be about ten times smaller than for the force
generated by rotor of an infinite length in open water
conditions [1]. However the field experiment showed
that this force is large enough to compensate yawing
moment generated by the stern rudder turned by 10°
[3].
3.1 Field experiments on the drift angle control using bow
rotor rudder
The field experiment was carried out on Lake Silm at
the Ilawa Ship Handling Research and Training Centre
[20]. The bow rotor rudder was installed on the barge
bow-shaped attachment to the ship model. The
experimental test setup is presented in Figure 4.
Figure 4. The experimental setup with bow rotor rudder.
The main particulars of the ship model, barge bow-
shaped attachment and rotor parameters are presented
in Table 1.
Table 1. Main particulars of the ship model, bow attachment
and rotor.
Main particulars of ship model
Parameter
Value
Length (m)
12.20
Breadth (m)
2.00
Draft (m)
0.64
Model scale
1:24
Bow attachment parameters
Parameter
Value
Length LOA [m]
2.20
Breadth B [m]
2.00
Draft T [m]
0.64
Bow scale
1:24
Rotor parameters
Parameter
Value
Height H [m]
0.60
Cylinder diameter D [m]
0.11
Screen diameter d [m]
0.19
Rotational speed r [RPM]
0-570
RC drive power [W]
1000
The program of experiments included trials with
different model speeds and different bow rotor rudder
rotational speeds. The measured model course, course
over ground CDG and drift angle β for model speeds
from 0.52 m/s to 1.08 m/s are presented in Table 2.
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Table 2. Test results
Lp.
v
r
Course
COG
β
m/s
RPM
deg
deg
deg
1
0.52
300
313.92
328.33
14.40
2
0.52
300
313.52
327.63
14.12
3
0.52
300
136.71
151.32
14.61
4
0.53
300
135.54
150.77
15.24
5
0.53
300
313.14
328.08
14.94
6
0.62
300
313.90
327.61
13.71
7
0.69
300
313.02
322.74
9.72
8
0.71
300
132.68
146.12
13.44
9
0.73
300
128.82
142.87
14.05
10
0.75
300
310.68
325.34
14.66
11
0.79
300
312.84
327.53
14.69
12
0.93
550
312.76
328.17
15.41
13
0.94
500
136.42
151.92
15.49
14
0.96
400
312.66
328.72
16.06
15
0.96
400
136.16
150.50
14.33
16
1.00
300
313.40
326.02
12.62
17
1.00
300
131.32
139.10
7.78
18
1.08
300
315.60
325.45
9.86
The dependence between model velocity and drift
velocity are presented in Figure 5.
Figure 5. Drift velocity dependent on model velocity and
bow rotor rudder rotational speed.
During the field experiments at 300 RPM a linear
increase in the drift angle was observed from 0.52 m/s
to 0.79 m/s. At higher model speeds the flow
separation occurring on the rotor was the reason of
drift velocity decrease. At higher rotational speeds of
400 rpm, 500 rpm, 550 rpm, an increase in drift speed
of about 20% was observed, however, with this
combination of rotor speed and model speed, strong
rotor vibrations interrupted the experiment.
3.2 Reduction of drift angle
Using a bow rotor rudder when navigating inland
waterways can significantly improve the
maneuverability of a push-barge convoy [5]. The
maneuvering space (lane width) can be reduced thanks
to the ability of the convoy to move sideways in
parallel, allowing to maintain a constant course. The
test of maintaining a constant heading, navigating in
leading lights, was conducted with the bow rotor
rudder rotating clockwise at 300 rpm. The stern rudder
was turned 8°–10° to portside to compensate for the
bow rotor-generated yawing moment. The trajectory of
the model (point at amidships) plotted during the trial
is presented in Figure 6.
Figure 6. Model trajectory during steady course trial.
Developed on the basis of [3].
The examples of possible reduction of a push
convoy manoeuvring space in inland navigation by
drift angle control using the bow rotor rudder are
presented in Figure 7.
Figure 7. Examples of possible reduction of a push convoy
manoeuvring space in inland navigation by drift angle
control using the bow rotor rudder - manoeuvring in a river
bend: (a) meeting, (b) overtaking, (c) turning with ruder only
- pivot point moved ahead in the river bend, (d) turning with
rotor only - pivot point moved astern.
4 CONCLUSIONS
The main factor that allows for reducing the space
requirement in river navigation is the reduction of the
vessel's drift angle during turning, overtaking, meeting
300 RPM
550 RPM
500 RPM
400 RPM
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.52
0.52
0.52
0.53
0.53
0.62
0.69
0.71
0.73
0.75
0.79
0.93
0.94
0.96
0.96
1.00
1.00
1.08
v
d
[m/s]
v [m/s]
1006
and passing maneuvers, because the vessel does not
have to turn, but can move sideways only.
Other factors, like high or low water levels, poor
visibility, poor fairway conditions, strong currents,
irregular banks, ecological demands and helmsman
experience - skills and stress levels, directly influence
the necessary dimensions of the waterway. The direct
and indirect impacts are related to the safety and ease
of navigation.
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